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#include "Wire.h"
#include "I2Cdev.h"
#include "MPU6050.h"
MPU6050 accelgyro;
unsigned long now, lastTime = 0;
float dt; //微分時間
int16_t ax, ay, az, gx, gy, gz; //加速度計陀螺儀原始數據
float aax=0, aay=0, agx=0, agy=0, agz=0; //角度變量
long axo = 0, ayo = 0, azo = 0; //加速度計偏移量
long gxo = 0, gyo = 0, gzo = 0; //陀螺儀偏移量
float pi = 3.1415926;
float AcceRatio = 16384.0; //加速度計比例系數
float GyroRatio = 131.0; //陀螺儀比例系數
uint8_t n_sample = 8; //加速度計濾波算法采樣個數
float aaxs[8] = {0}, aays[8] = {0}; //x,y軸采樣隊列
long aax_sum, aay_sum; //x,y軸采樣和
float a_x[10]={0}, a_y[10]={0} ,g_x[10]={0} ,g_y[10]={0}; //加速度計協方差計算隊列
float Px=1, Rx, Kx, Sx, Vx, Qx; //x軸卡爾曼變量
float Py=1, Ry, Ky, Sy, Vy, Qy; //y軸卡爾曼變量
void setup() {
Wire.begin();
Serial.begin(9600);
accelgyro.initialize(); //初始化
unsigned short times = 200; //采樣次數
for(int i=0;i<times;i++){
accelgyro.getMotion6(&ax, &ay, &az, &gx, &gy, &gz); //讀取六軸原始數值
axo += ax; ayo += ay; azo += az; //采樣和
gxo += gx; gyo += gy; gzo += gz;
}
axo /= times; ayo /= times; azo /= times; //計算加速度計偏移
gxo /= times; gyo /= times; gzo /= times; //計算陀螺儀偏移
}
void loop(){
unsigned long now = millis(); //當前時間(ms)
dt = (now - lastTime) / 1000.0; //微分時間(s)
lastTime = now; //上一次采樣時間(ms)
accelgyro.getMotion6(&ax, &ay, &az, &gx, &gy, &gz); //讀取六軸原始數值
float accx = ax / AcceRatio; //x軸加速度
float accy = ay / AcceRatio; //y軸加速度
float accz = az / AcceRatio; //z軸加速度
aax = atan(accy / accz) * (-180) / pi; //x軸對于水平面的夾角
aay = atan(accx / accz) * 180 / pi; //y軸對于水平面的夾角
aax_sum = 0; // 對于加速度計原始數據的滑動加權濾波算法
aay_sum = 0;
for(int i=1;i<n_sample;i++){
aaxs[i-1] = aaxs[i];
aax_sum += aaxs[i] * i;
aays[i-1] = aays[i];
aay_sum += aays[i] * i;
}
aaxs[n_sample-1] = aax;
aax_sum += aax * n_sample;
aax = (aax_sum / (11*n_sample/2.0)) * 9 / 7.0; //角度調幅至0-90°
aays[n_sample-1] = aay; //此處應用實驗法取得合適的系數
aay_sum += aay * n_sample; //本例系數為9/7
aay = (aay_sum / (11*n_sample/2.0)) * 9 / 7.0;
float gyrox = - (gx-gxo) / GyroRatio * dt; //x軸角速度
float gyroy = - (gy-gyo) / GyroRatio * dt; //y軸角速度
agx += gyrox; //x軸角速度積分
agy += gyroy; //x軸角速度積分
/* kalmen start */
Sx = 0; Rx = 0;
Sy = 0; Ry = 0;
for(int i=1;i<10;i++){ //測量值平均值運算
a_x[i-1] = a_x[i]; //即加速度平均值
Sx += a_x[i];
a_y[i-1] = a_y[i];
Sy += a_y[i];
}
a_x[9] = aax;
Sx += aax;
Sx /= 10; //x軸加速度平均值
a_y[9] = aay;
Sy += aay;
Sy /= 10; //y軸加速度平均值
for(int i=0;i<10;i++){
Rx += sq(a_x[i] - Sx);
Ry += sq(a_y[i] - Sy);
}
Rx = Rx / 9; //得到方差
Ry = Ry / 9;
Px = Px + 0.0025; // 0.0025在下面有說明...
Kx = Px / (Px + Rx); //計算卡爾曼增益
agx = agx + Kx * (aax - agx); //陀螺儀角度與加速度計速度疊加
Px = (1 - Kx) * Px; //更新p值
Py = Py + 0.0025;
Ky = Py / (Py + Ry);
agy = agy + Ky * (aay - agy);
Py = (1 - Ky) * Py;
/* kalmen end */
Serial.print(agx);Serial.print(",");
Serial.print(agy);Serial.println();
}

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